A Commutative Algebra for Oriented
نویسنده
چکیده
Let V be a vector space of dimension d over a field K and let A be a central arrangement of hyperplanes in V . To answer a question posed by K. Aomoto, P. Orlik and H. Terao construct a commutative K-algebra U(A) in terms of the equations for the hyperplanes ofA. In the course of their work the following question naturally occurred: ◦ Is U(A) determined by the intersection lattice L(A) of the hyperplanes ofA? We give a negative answer to this question. The theory of oriented matroids gives rise to a combinatorial analogue of the algebra of Orlik–Terao, which is the main tool of our proofs.
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